Welcome to the forum. You're our first Finn! Although despite the name it's not just Brits here.
You've asked quite a lot of questions and I'd like to take the time to reply properly. Maybe even make an FAQ page as people tend to be interested in the same things.
I'll be happy to meet you when you come to Delhi if you'd like. I can show you around and answer some of your questions in more detail. (I'm meeting Sally Ann tomorrow, who also posted here for advice.)
Briefly, loads of expats live in Vasant Vihar but there are other places you may want to consider which are nearer the school.
Internet connections are available but fairly slow. I have two ISPs so that when one doesn't work, with luck the other will. You'll probably need a generator to power your computer(s) when there's no city power, because there are frequent power cuts, and a UPS. It's not too bad - we're managing to run our website from here. I've heard that some ISPs are introducing broadband services now so you may be lucky enough to get that.
Delhi Network, as far as I know, doesn't yet have a website. I'm friends with their president although I'm not a member myself. They have an office in the Hyatt hotel which is staffed on a part-time basis.
As for bowling, sorry I don't know anything about that.
I'll try to find out more and it's possible that Sally Ann will have more information for you about schools etc, after she's finished her fact-finding mission here. Stay in touch.
Again, welcome, it's great to have another nationality on here.